I need an explanation for this Engineering question to help me study.

What are cryptography and cryptanalysis?

What is earlier reason for the use of cryptography?

• Fermat’s theorem and Euler’s theorem are the two theorems that play important roles in public-key cryptography. Explain each theorem in details their roles in public-key cryptography. 
• Explain the Chinese Remainder Theorem that have been discovered by the Chinese mathematician Agrawal in 100 A.D.